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Unformatted text preview: Print: First Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Last Name: . . . . . . . . . . . . . . . . . . . . . . . . . .. Student Number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . University of Toronto
Faculty of Applied Science and Engineering Final Examination — December 12, 2005 ECE253F — Digital and Computer Systems Examiner — Parham Aarabi 1. There are 6 questions and pages. Do all questions. The total number of marks is 100.
The duration of the test is 2 hours 30 minutes. 2. ALL WORK IS TO BE DONE ON THESE SHEETS! Use the back of the pages if
you need more space. Be sure to indicate clearly if your work continues elsewhere. ' 3. Open book  Exam Type D. Only authorized photocopies of copyrighted material are allowed.
A photocopy of Appendix A for Verilog is permitted. 4. All calculators permitted. 5. Please put your ﬁnal solution in the appropriate spaces. A big space does not necessarily
mean a long answer is required. 6. Place your student card on your desk
1 [10]
2 [10]
3 [20]
4 [10]
5 [20]
6 [30] Total [100] l Page 1 of 11 [10 marks] 1. Funwith oscillations. [5 marks] [5 marks] a) Design a ring oscillator with a frequency of 20MHz. Assume you have an unlimited
supply of NOR gates that have a propagation delay of 5ns. Draw the circuit diagram of
your design. b) Still using your unlimited supply of NOR gates, add an activehigh reset signal to the
oscillator you designed in part a) (i.e. the oscillator’s output is reset to 0 when the signal
Rst is high). Page 2 of 11 [10 marks] 2. Using an 8—bit adder (deﬁned below), write a Verilog module that multiplies a 4bit number
num by 9. If the result is divisible by 4, the 1bit output flag is 1, otherwise the output is 0. module adder8 (cin, x, y, s, cout);
input cin;
input [7:0] x, y;
output [7:0] 5;
output cout; endmodule module mymodule (num, ﬂag);
input [3:0] num;
output ﬂag; endmodule Page 3 of 11 [20 marks] 3. Youvare to design a ﬁnite state machine with two inputs and one output. The inputs :1: and [5 marks] [5 marks] y provide two numbers (of unknown bit length) in a serial fashion (i.e. one bit of the ﬁrst
number arrives at the input at: every clock cycle, and one bit of the second number arrives at
the input y every clock cycle). The output 22 should only be set to a 1 if the total number of ‘1’ bits in :1: minus the total
number ‘1’ bits in y, modulo 3, is equal to 0. (for example, if six 1’s have been received from
x, and three 1’s from y, or if nine 1’s have been received by m, and zero 1’s by y, then the.
output 1) should equal 1). a)_ Draw the Moore state diagram using only three states. Include a reset signal. b) Draw the state transition table assuming that you will be using ONLY two DFFs. Page 4 of 11 [10 marks] c) Derive minimized expressions for the FSM’s next state and output. Draw the corre
sponding logic circuit for the entire system. Page 5 of 11 [10 marks] 4. Write a 68k assembly program that computes the factorial of a number, deﬁned as n! =
n(n — 1)... 1, WITHOUT using any instruction that has the character ‘u’ in it (i.e. you
cannot use mulu, muls, sub, Assume that the number is stored in memory location N,
and “store the ﬁnal result in memory location FINRES. Page 6 of 11 [20 marks] 5. Stranded on a stormprone and earthquakeprone island, you manage to salvage a 68k proces— [8 marks] sor board, several batteries, and lots of AND, OR, and NOT gates as well as tri—state buffers.
After years of research you ﬁnd a mysterious plant that can predict earthquakes and storms. This plant has two 8neuron bundles, with each neuron either being ‘on’ (i.e. having a high
voltage) or ‘off’ (i.e. low votlage). You ﬁnd that 7 times the number of ‘on’ neurons in the ﬁrst bundle will tell you roughly how
many days there are before an earthquake. You also ﬁnd that the number of ‘on’ neurons in
the second bundle, squared, tells you roughly how many days there are before a storm. a) Design the interface circuit to connect the plant neurons to your 68k processing bus.
Use the address $10000 for the plant. Page 7 of 11 [12 marks] b) Write a 68k assembly program that reads the information from the plant and stores the
number of days before an earthquake in D0 and the number of days until a storm in D1. Page 8 of 11 [8 marks] ORG DS.L DS.L ORG
MOVEAL
MOVE.L
MOVE.L
MOVE.L
BSR BRA THESTK STUCK ORG
MOVEL
SUBL
CMPL
BEQ
MOVEL
MULUL
ADDL
BSR
MOVEL
RTS SQUARECURSE ENDCURSE a) After the program gets stuck in the inﬁnite loop at STUCK, what is the value of D0 and [30 marks] 6. Consider the following 68000 assembly program: $10000 99 ; initializing the stack
1 $20000 #THESTK,A7 #6,D0 #0,D1 #6,D2 SQUARECURSE STUCK $20040
D24An
#LDO
#0D0
ENDCURSE
D0D2
DZD2
DzDi
SQUARECURSE
(AU+JD ;just a simple unsigned multiply D1? Note that the ‘mulu.l’ instruction is a simple unsigned multiply. Page 9 of 11 [6 marks] .. continuation of a). b) Assuming that all branch instructions (i.e. BSR, BEQ) take 1 word (16 bits) of mem— ory, ﬁnd out the memory addresses of each instruction, including STUCK as well as
ENDCURSE. Page 10 of 11 [8 marks] 0) Show the exact contents of the stack after the BBQ ENDCURSE branch is taken (not
in the ﬁrst iterations when the BBQ ENDCURSE branch is not taken). d) You realize that that this operation could be done much more efﬁciently by using a single
, loop without subroutines. Rewrite the program so that the end result in D0 and D1 is
the same, but using only a single loop without subroutines. Page 11 of 11 ...
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 Winter '08
 B.wang

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